Section 12.2 – Vectors
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Given the points \(A(-2,4,2)\) and \(B(3,0,8)\), find \(\overrightarrow{AB}.\)
\(\overrightarrow{AB}=\langle 5,-4,6 \rangle\)
2. Given \(\mathbf{a} = \langle 1, -1, 5 \rangle\) and \(\mathbf{b} = \langle -3, 2, 1 \rangle\), find \(|\mathbf{a} + 2\mathbf{b}|.\)
\(|\mathbf{a} + 2\mathbf{b}| = \sqrt{83}\)
3. Find the vector that has the same direction as \(\mathbf{a} = 2\mathbf{i} + \mathbf{j} - 2\mathbf{k}\) but has length \(5.\)
\(\dfrac{10}{3}\mathbf{i} + \dfrac{5}{3}\mathbf{j} - \dfrac{10}{3}\mathbf{k}\quad \) or \( \quad \left< \dfrac{10}{3}, \dfrac{5}{3}, -\dfrac{10}{3} \right>\)